Cauchy problem for a nonlinear wave equation with nonlinear damping and source terms
โ Scribed by Grozdena Todorova
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 108 KB
- Volume
- 41
- Category
- Article
- ISSN
- 0362-546X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
For the Cauchy problem for the nonlinear wave equation with nonlinear damping and source terms we define stable and unstable sets for the initial data. We prove that, if during the evolution the solution enters into the stable set, the solution is global and we are able to estimate the decay rate of
## Abstract In this paper we consider a nonlinear wave equation with damping and source term on the whole space. For linear damping case, we show that the solution blows up in finite time even for vanishing initial energy. The criteria to guarantee blowup of solutions with positive initial energy a
We study the nonlinear wave equation involving the nonlinear damping term \(u_{i}\left|u_{t}\right|^{m-1}\) and a source term of type \(u|u|^{p-1}\). For \(1<p \leqslant m\) we prove a global existence theorem with large initial data. For \(1<m<p\) a blow-up result is established for sufficiently la